- Experiment 2 Implementation Of Boolean Functions With Digital Gates 2 1 Objective The Objective Of This Experiment Is To 1 (144.85 KiB) Viewed 38 times
- Experiment 2 Implementation Of Boolean Functions With Digital Gates 2 1 Objective The Objective Of This Experiment Is To 2 (79.83 KiB) Viewed 38 times
- Experiment 2 Implementation Of Boolean Functions With Digital Gates 2 1 Objective The Objective Of This Experiment Is To 3 (100.78 KiB) Viewed 38 times
EXPERIMENT 2 IMPLEMENTATION OF BOOLEAN FUNCTIONS WITH DIGITAL GATES 2.1 OBJECTIVE The objective of this experiment is to write minterm and maxterm equation for given table. Simplify the equations to draw the circuit. 2.2 EQUIPMENT LIST • Digital Training set Y-0039, • Logic Gates : 7408 AND gate, 7404 INVERTER, 7432 OR gate 2.3 THEORY The behavior of a digital circuit is defined by a set of Boolean equations, which has only binary variables. The Boolean operators have similarities with ordinary integer operators. AND can be regarded as multiplication and OR can be regarded as addition. The precedence of operations in a Boolean equation is similar to the precedence in ordinary arithmetic operation (Table2.1). The value of a Boolean equation is correctly evaluated if these precedence rules are obeyed. Table 2.1 Symbol ( Precedence decreases Name COMPLEMENT (ENOT) Parantheses AND OR 0 + 2.3.1. Direct Implementation of a Boolean Function Implementation level is actually the depth of the circuit. The depth of a circuit provides direct information about the latency of the circuit. Latency (a) is the time spent between the time when a specific input value is fed to the circuit (ti) and the time when the related value is obtain at the output (to): 1 = to-ti One can easily say that the latency of the circuit is directly proportional with the implementation level of the circuit. Then, it can be also claimed that as the implementation level is decreases, the circuit will respond faster to the changes at its inputs. 2.3.2. Canonical Two-Level Implementation of a Boolean Function Truth tables are very helpful to build two-level circuits for a Boolean function. There are two forms of two- level implementations: SOP (sum-of-products) and POS (product-of-sums).
Level 2 Level 1 POS (Product of Sums) 12 6 SOP (Sum of Products) Đ 8 Figure 2.1 Canonical SOP (sum-of-product) A minterm mi is defined as a product term formed by ANDing the inputs of Row I of the truth table. For each input x; that is zero on the truth table, the input x¡ appears in its complement form in the related minterm. If xj is 1 on the truth table, the input xj appears as it is in the related minterm. For example, miis x'ı x'2X3. See minterms list in Table 2.2. Table 2.2 Inputs Output X1 X2 X3 Z Row 0 → 0 0 0 mo= x'ıx'2x'3 Row 1 → 0 0 1 Row 2 → 0 1 0 Row 3 → 0 1 1 mi= x'ix'2x3 m2= x'1 x2x's m3= x'1 X2 X3 m4= X1 X'z x'3 ms= X1 X'z x3 Row 4 → 1 0 0 Row 5 → 1 0 1 Row 6 → 1 1 0 m6= X1 X2 X'3 Row 7 → 1 1 1 m7= X1 X2 X3
Canonical POS (product-of-sums) A maxterm Mi is defined as a product term formed by ORing the inputs of Row i of the truth table. For each input xi that is 1 on the truth table, the input xj appears in its complemented form in the related maxterm. For example, Mi is x1 + x2 + x's. 2.4 PRELIMINARY WORK 1. What is minterms list? 2. Find the minterm equation for the XOR gate above. 3. What is maxterms list? 4. Find the maxterms equation for the XOR gate above. 5. How many inputs and outputs are there in Table 2.2 2.5 PROCEDURE 1. Find the Boolean minterm equation for the given table (Table 2.3). 2. Draw the circuit. Table 2.3 Inputs Output X1 X2 X3 0 0 0 Row 0 → Row 1 → 0 0 1 O NOOO Row 2 → 0 1 0 0 Row 3 → 0 1 1 1 0 0 0 1 1 Row 4 → 1 Row 5 → 1 1 Row 6 → 1 0 1 Row 7 → 3. Simplify the equation. 4. Draw the circuit only with AND, OR, and INVERTER gates. 5. Realize the circuit using Digital Training Set Y-0039 and the gates above. 6. Show your circuit and outputs to the lab. Instructor. 7. Find the Boolean maxterms equation for the given table (Table 2.3). 8. Draw the circuit.